A. 36°, B. 90°, C. 36°, D. 90°, E. 54°, F. 126°, G. 54°, H. 126°, I. 54°, J. 36°, K. 144°, L. 36°, M. 144°
First, let’s go over the information given:
The two diagonal lines are parallel (as denoted by the symbols),
m∠3=54°,
m∠2=90° (the square symbol in the corner means it’s a right angle).
(C). Angles 2, 3, and 4, create a horizontal line. The sum of angles on a straight line have a sum of 180°. Since we know the measures of angles 2 and 3, we can find angle 4 by subtracting them from 180°:
m∠4 = 180° - 90° - 54°
m∠4 = 36°
(D). Angle 5 is a right angle, so m∠5 = 90°
(i). Angle 3 and 10 are alternate exterior angles, so they are congruent.
m∠10=54°
(H). Angle 9 and 10 will have a sum of 180° as they create a straight line.
m∠9 = 180° - m∠10
m∠9 = 180° - 54°
m∠9=126°
(E). You found that m∠6=54° and m∠8=54° because angles 6 and 8 are alternate interior angles .
(A). Angles 1 and 6 are complimentary and will create a right angle. Angle 1 is also congruent to angle 13 as they are alternate exterior angles. Subtract angle 6 from 90° and:
m∠1 = 36°
(L). Angle 4 and 13 are corresponding angles, so they are congruent.
m∠13=36°
(K). Angles 12 and 13 are supplementary angles, meaning the two angles have a sum of 180°.
m∠12 = 180° - m∠13
m∠12 = 180° - 36°
m∠12 = 144°
(J). Angles 5,8,11 are the interior angles of a triangle. The sum of the inner angles of a triangle is 180°. So, m∠11 + m∠8 + m∠5 = 180.
m∠11 = 36°.
(M). Angles 11 and 14 are also supplementary. m∠14 = 180° - 36°
m∠14 = 144°
(F). Angle 6 and 7 are same side interior angles. This means they are supplementary and have a sum of 180°.
m∠7 = 180° - m∠6
m∠7 = 180° - 54°
m∠7 = 126°
(This can also be verified by checking the sum of angle 2 and 3 as their combined angle corresponds to the same position of angle 12 (90+54=144)).
Hope this helps !